added Dijkstra’s Algorithm

Author: sourav-naskar

CPP/graph_tree/Dijkstra_Algorithm.cpp

@@ -0,0 +1,55 @@
+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+	int n=5,m=6,source=1;
+	vector<pair<int,int> > g[n+1]; 	// assuming 1 based indexing of graph
+	// Constructing the graph
+	g[1].push_back({2,2});
+	g[1].push_back({4,1});
+	g[2].push_back({1,2});
+	g[2].push_back({5,5});
+	g[2].push_back({3,4});
+	g[3].push_back({2,4});
+	g[3].push_back({4,3});
+	g[3].push_back({5,1});
+	g[4].push_back({1,1});
+	g[4].push_back({3,3});
+	g[5].push_back({2,5});
+	g[5].push_back({3,1});	
+	// Dijkstra's algorithm begins from here
+	priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int>>> pq;
+	vector<int> distTo(n+1,INT_MAX);//1-indexed array for calculating shortest paths
+	distTo[source] = 0;
+	pq.push(make_pair(0,source));	// (dist,source)
+	while( !pq.empty() ){
+		int dist = pq.top().first;
+		int prev = pq.top().second;
+		pq.pop();
+		vector<pair<int,int> >::iterator it;
+		for( it = g[prev].begin() ; it != g[prev].end() ; it++){
+			int next = it->first;
+			int nextDist = it->second;
+			if( distTo[next] > distTo[prev] + nextDist){
+				distTo[next] = distTo[prev] + nextDist;
+				pq.push(make_pair(distTo[next], next));
+			}
+		}
+	}
+	cout << "The distances from source " << source << " are : \n";
+	for(int i = 1 ; i<=n ; i++)	cout << distTo[i] << " ";
+	cout << "\n";
+	return 0;
+}
+
+/*
+Output:
+
+The distances from source 1 are :
+0 2 4 1 5
+
+Time Complexity: O((N+E)*logN). Going through N nodes and E edges and log N for priority queue
+
+Space Complexity: O(N). Distance array and priority queue
+*/
+
+////contributed by Sourav Naskar